가다머의 명제논리 - 기하학은 그 스스로의 기하학이다
Gadamer’s Propositional Logic - Geometry is geometry itself
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나는 이 논문에서 기하학적 명제논리를 논증한다. 기하학적 명제논리를 논증하기에 앞서, 나는 유클리드 기하학과 플라톤 기하학은 서로 양립할 수 없다는 가다머의 논거를 제시한다. 가다머가 보기에 철학의 명제논리들은 기하학에서와 같이 증명되는 것이 아님에도 불구하고 누구도 의심 없이 유클리드 기하학의 논리명제를 완벽한 하나의 논리형식으로 간주했다. 본 논문은 가다머의 기하학적 명제논리가 유클리드의 명제논리와는 다른 독특한 논리형식에 그 토대를 두고 있다고 제안한다. 따라서 이 논문은 다음 두 논제에 대한 물음이다. 첫 번째, 도대체 하나의 기하학체계에서 기하학적 성질로서 증명되는 범위는 어디까지인가? 두 번째, 우리가 소위 철학의 문제라고 간주하는 것은 유클리드 기하학을 철학의 문제로 끌어들임으로써 발생한 역설들이 아닌가? 나는 이 두 물음을 토대로 하여 나의 기하학적 명제논리가 이른바 기하학에 대한 서로 다른 ‘논리의 자기해석’임을 논증한다.
Abstract
In this paper, I argue for a geometric propositional logic. Before arguing for geometric propositional logic, I present Gadamer’s argument that Euclidean geometry and Plato’s geometry possess logically incompatible propositional forms. According to Gadamer assumption, although the propositional logics of philosophy are not proven in the same way as in geometry, no one ever doubted that the propositions of Euclidean geometry were regarded as a perfect logical form. I suggest that Gadamer’s geometric propositional logic is based on a unique logical form that is different from Euclidean propositional logic. Therefore, this paper is an inquiry into the following two propositions. First, to what extent can properties be proven as geometric within a single geometric entity? Second, aren’t the so-called problems of philosophy the paradoxes that arise from bringing Euclidean geometry into the realm of philosophical problems? Based on these two questions, I argue that my geometric propositional logic represents a so-called “logical self-interpretation” of geometry.
참고문헌 (32)
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